Application of GMLS-based numerical manifold method in buckling analysis of thin plates

Abstract

This paper applies the GMLS-based numerical manifold method (NMM) in analyzing the buckling behaviors of thin plates. The numerical manifold method (NMM), deploying two cover systems, namely the mathematical cover (MC) and physical cover (PC), has been successfully employed in the continuum and discontinuum deformation analysis. In this study, the MC system is constructed with influence domains in generalized moving least squares (GMLS) interpolation rather than the commonly-used finite element meshes, which is especially fitted for the fourth-order problems with rotational degrees of freedom and simplifies the possess of generating physical cover system. Moreover, the GMLS-based NMM can be readily utilized to treat plates with arbitrary complex geometry and openings without resorted to those complicated criteria and tailored operations. A series of numerical experiments concerning buckling analysis for thin plates with various shapes and cutouts have been performed, thus validating the effectiveness and accuracy of the proposed GMLS-based numerical manifold method.